# How to find difference between data recorded for 1431 variables for X subjects, across 3 time points?

I am doing research using magnetoencephalography (MEG). I'm performing coherence analysis which, briefly, is a measure of neuronal synchronicity and functional connectivity.

For each subject scanned with MEG, we populate a predefined set of 1431 variables, each representing the "synchronicity" between brain region pairs, on a continuous scale from 0 to 1.

I have $$X$$ number of subjects whom each got a MEG scan at three time points: $$A$$, $$B$$, and $$C$$. Our treatment was applied at point $$B$$.

I would like to measure our treatment effect on the coherence of my subjects across these time points, and then compare that to healthy controls. What methods would be appropriate for modeling these differences?

• My n = 4 subjects. I realize it is a small sample size, but since each subject has 1431 variables recorded, I'm not sure how to proceed with my data. – Abdullah Alshammaa May 25 '19 at 18:50
• If all 4 got the treatment at time B, who would the healthy controls be? – AdamO May 25 '19 at 19:26
• i have a set of 4 control subjects who got the scans at 1 point. Eventually I'd like to compare how my patients are doing at points A, B, C, compared to controls. – Abdullah Alshammaa May 25 '19 at 20:42
• Well they aren't really controls (in a traditional sense) if they're not assessed in the same way as the intervention group. But you can make some assumptions that their neuroconnectivity remains unchanged between iterations. – AdamO May 25 '19 at 20:48

Despite measuring functional connectivity at over 1,000 locations, the appropriate "n" for the sample is 8 (or even smaller if you use the analysis I propose). So the analysis is likely under powered, that just means you have to be very cautious in how you interpret the findings: a significant result can be driven by one outlying person, and a non-significant result tells you very little.

Deciding on the functional effect of treatment is important. What will be the influence of treatment at time $$C$$? Some modeling effects of longitudinal treatment effect are are

• pre-post, such that at any time point after administration of treatment, the effect is expected to stay the same (expected response same at time $$B$$ or $$C$$),
• a growth or learning effect where the response at time $$C$$ is expected to be greater than at time $$B$$,
• a washout effect where the response at time $$C$$ is either between time $$B$$ and time $$A$$ or regresses completely to expected response at time $$A$$, or
• completely agnostic.

Once the effect of treatment is settled, I would approach this by fitting an ANCOVA. The control subjects cannot contribute to the analysis since you did not collect any post baseline measures. Reshape the data into a long format with one measure for each subject, each post-baseline time point, and each brain-region pair. Merge one-to-many the baseline values. Create indicators of time point, first post baseline vs. second post baseline.

The repeated measures at each site could be handled with a random intercept and possibly a random slope term to capture repeat measures at brain region pairs within subjects. You would include categorical effects of time, and adjust for baseline values. The interpretation of the time effects would be the average change from baseline.

• Thank you Adam! I'm using R for analysis, and utilizing tidyverse package. 1- I can use dplyr to melt my data to long format. However I didnt quite understand what you mean by merging one to many. 2- For controls, can they be compared to the baseline of my subjects only? – Abdullah Alshammaa May 26 '19 at 16:47